Gopalakrishnan Sarang, Vasseur Romain, Ware Brayden
Department of Physics and Astronomy, City University of New York College of Staten Island, Staten Island, NY 10314;
Physics Program and Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, NY 10016.
Proc Natl Acad Sci U S A. 2019 Aug 13;116(33):16250-16255. doi: 10.1073/pnas.1906914116. Epub 2019 Jul 30.
We compute the spin-structure factor of XXZ spin chains in the Heisenberg and gapped (Ising) regimes in the high-temperature limit for nonzero magnetization, within the framework of generalized hydrodynamics, including diffusive corrections. The structure factor shows a hierarchy of timescales in the gapped phase, owing to s-spin magnon bound states ("strings") of various sizes. Although short strings move ballistically, long strings move primarily diffusively as a result of their collisions with short strings. The interplay between these effects gives rise to anomalous power-law decay of the spin-structure factor, with continuously varying exponents, at any fixed separation in the late-time limit. We elucidate the cross-over to diffusion (in the gapped phase) and to superdiffusion (at the isotropic point) in the half-filling limit. We verify our results via extensive matrix product operator calculations.
在广义流体动力学框架内，包括扩散修正，我们计算了非零磁化强度高温极限下，海森堡和能隙（伊辛）区域中XXZ自旋链的自旋结构因子。由于各种尺寸的s自旋磁振子束缚态（“弦”），结构因子在能隙相中显示出时间尺度的层次结构。尽管短弦以弹道方式移动，但长弦由于与短弦的碰撞主要以扩散方式移动。这些效应之间的相互作用导致自旋结构因子在晚期极限下，在任何固定间距处呈现出异常的幂律衰减，且指数不断变化。我们阐明了在半填充极限下向扩散（在能隙相）和超扩散（在各向同性点）的转变。我们通过广泛的矩阵积算子计算验证了我们的结果。
